the radical rational…

in search of innovative ideas with a well-balanced approach for the math classroom

The Moving Walkway #julychallenge Post 19

As I am walking through the airport this morning, it was not crowded and had I been brave, I would have collected some data to enable me to create a nice little work-rate problem.

How much time does that moving walkway actually save me?

Scenario 1: walk the distance.
Scenario 2: ride the distance
Scenario 3: walk while riding
Hmmm…Scenario 4: while riding, walk against the moving walkway.

The next time I have an early flight, when it’s not crowded.  You bet I will be recording some times.

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Gum Container Repurposed Dice #julychallenge Post 18

Quickest post ever!

Got these dice at a Five Below store last summer.


Ice Breakers, Ice Cubes Gum container…perfect for storing!

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Setting Personal Social-emotional Goals pt. 2 #julychallenge Post #17

This morning as I responded to a commented from @bpagirls on my post about an Essential Questions Board, a thought hit me, so I typed it in my reply so I wouldn’t forget…

… I have just realized as I type, why not add a spot for personal-social goal-setting on my organizer for each student to set, write and reflect.

It stems back to this post and one of the 14 ways to think about good teaching post, 3. Include social-emotional learning goals as well as academic goals.

I got that I needed to do this, but I was not quite sure how to set and record these goals.  My plans are to include a place on the back of our unit organizer students receive at the beginning of each unit.  These are formatted in a booklet style to fit our INBs.  Students can set a personal/social goal to focus on for the duration of the unit. Ideally, following the SMART goal format.  Commit to it by writing it on their organizer.  I will ask to see it, but they may choose whether to share with a peer.  Wouldn’t it be great to have accountability partners for the unit? 

Throughout the unit or even at beginning of class, ask them to read it to themselves.  Maybe even allow someone to share their progress.  Revisit them as we end the unit and write a brief reflection:  How did I do?  Did I meet my goal?  If not, did I at least move toward it? What do I need to modify?  Follow the format: 2 stars and a wish for their quick-write reflection.  Celebrate their progress, maybe through our Shout-Out Board (more on that later).

I realize this type of goal setting may be tough for students… I am hoping after completing this task, it will allow for students to generate ideas.

Initially, I think goals can range from:
Improved / good attendance
Be to class on time
Being prepared for class
Completion of assignments
Asking for help
Asking questions or participating in class discussions.
Attend tutoring if needed
Work in a group with people I don’t know.
Share my ideas in class
Share my assessments and progress with parents/guardian
Choose better practice/study options
Listen to others ideas
Evaluate how my choices are impacting my learning.

Here is a sample of the back of my unit organizer.  I plan to insert personal goals below the unit reflection.  Here is an updated version of a complete unit organizer and student assessment tracker. Feel free to modify for use in your personal classroom. Thanks to Crazy Math Teacher Lady and Math = Love for inspiring through their posts?


My next task is to locate a fill-in the blank for a SMART to include on the first unit.  Kind of a madlibs style to get us started.

If you have a system in place or use LIM or AVID in your school, I welcome input and suggestions.

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Essential Questions for my Walls #julychallenge Post 16

4.  Translate learning goals into meaningful, interesting questions and challenges.

What if we thought about our teaching in terms of exploring open-ended questions that are interesting and meaningful to our students? What if we put “essential” questions on the board at the beginning of units and lessons, discussed with our students why they are important and meaningful, and then referred to them throughout the unit?

Is an excerpt from this post.  Along with posts from Anna and Kate, I know this is an area of needed growth in my planning.

For several days, I’ve been bugged by the lack of interesting bulletin boards in my classroom.  It bothers me that I am satisfied with sticking a motivational poster or favorite quote up for the entire year. I want something interactive, that has potential to impact student learning. 

Apparently my frustration in a tweet got into @druinok’s mind as well.  There have been some good discussions and even great ideas as a result of her post, yet it didn’t seem to be what I was looking for.

The excerpt above was it!  Why not have an essential questions board?  As we begin a unit, post to share our EQs, offer post-its for students to add to the board as we progress, revisit throughout the unit and again as a springboard for reflection as we end.

I believe this is one idea that will meet all of my goals.  It also supports a thinking environment from this #makthinkvis post.  I am looking forward to sharing more on the progression of this idea.


Social-Emotional Learning Goals #julychallenge Post 15

Still addressing 14 ways of thinking about good teaching from this post…

3.     Include social-emotional learning goals as well as academic goals.

It can be easy as a teacher to get wrapped up in student assessment data.  We must continually keep focused on the whole-student.  I always enjoy reading @druinok’s post on her experiences with AVID- Advancement Via Individual Determination.  To my understanding, it provides students with a system that will enable them to achieve more, be aware of choices and resources and work toward their post-secondary goals.  It provides them with academic structures as well as a mentor for accountability.

Many years ago, when I first began teaching in our freshman wing, The DOCK, our goal was to instill self-Discipline,  Organizational skills, develop positive Character traits and enhance student Knowledge through learning.  Our first few years were a huge success, but I never understood why it didn’t continue throughout the remainder of the school. Being out of the DOCK now, I terribly miss our weekly meetings to discuss options and strategies for struggling students, both discliplinary and acsdemically. 

After talking with some colleagues, their view of the DOCK had been tainted by comments others had made.  This made me sad because at the very heart of our collaboration was caring for students-the whole student.  Since I am no longer with that team, I must find ways to continue those positive practices.

I began using the INBs as a measure for helping students stay organized, developing reflection and study tools that can carry through their education.  I learned about Cornell notes through @druinok’s blog and shared the idea with some colleagues.  I value what CN can do in helping students learn and achieve.  I have observed students owning their INBs which leads to better effort in class and studying.

We also used excerpts from Covey’s 7 Habits for Highly Effective Teens book to drive our charachter models.  Each month, we would do an activity and focus on a trait specific to a given habit.  This summer, our school has participated in a 3-day Leadership training, focused on the 7 habits.  Our GRIT team has been meeting weekly to plan and outline school wide activities based on our shared goals.  I see this as a positive thing for our school culture and the possibility of having major impact on students as well.

Recently, I have noticed employee tshirts, one at a restaurant, “I love my job!” on the back and at a grocery with “Glad you’re here!” on the front.  Along with a poster “You are important!” – all of these may go without saying, but why not voice them?  I am a firm believer that my attitude rubs off on the students. 


Its fun to treat them as well.  I brought caramel apple suckers to an entire class one time because a student had been there for an entire week.  What happened next? The class began encouraging her too and the was a marked turnaround in her attendance and effort the second semester. 

Some ways I plan to make this happen:
Taking notice when they are at school.
Letting them know they were missed when they were absent.
An email or phone call to parents to pat them on the back. (Five on Friday)
Meet them at the door, good morning and a smile.
High fiving a small achievement. 
A note on the back of a paper to tell them I am proud of them. 
None of those things cost a dime. 

By holding them accountable, having conversations with them individually about their progress and effort or lack of, they become more aware of the impact of their actions.  Showing them their benchmarks and having a discussion about what they can do to improve.  Then letting them write their own goal and 2 things they plan to do to meet that goal.
But don’t stop there.  Revisit their goal often to remind them, keep them on track.  Most importantly, celebrate those small successes toward the end goal can be powerful motivation.

What are some ways you enhance the social-emotional growth of your students?


My Experience with Counting Circles #julychallenge Post 14

Still addressing 14 ways of thinking about good teaching from this post

2.  Plan goals for both the long term and the short term.

My number 1 goal is to help students grow – personally and academically.  My wish is that they leave my classroom believing in themselves, more self-confident than when they entered. 

Ideally, I do want every student to reach proficiency, but I am also a realist.  When students come to me with *ACT-PLAN scores in the 10-14 range, proficiency is not an immediate goal…growth is, pure and simple.  My class becomes the stepping stone to reach proficiency.  Students in this range generally have major gaps in number reasoning.  They are just now beginning to develop understanding and knowledge of assessed skills.

Last year, I wanted to use accessible tasks to begin each day…Counting Circles, Number Talks (pg 4 of link) and my post, Estimation180, and Visual Patterns were staples in my Algebra 2 classes.  Students in these classes ranging from ACTPLAN scores from 10 to 23-wide range of abilities and varied confidence levels.  These tasks were approachable for all students and I feel helped in developing number sense which allowed several students to make significant gains on thier ACT.

Counting Circles (Thanks to Sadie!) was very popular in both classes.  We literally got out of our desks to create a “circle” around the room. Yes, it seemed trivial at first, but I was able to see student confidence grow as they strengthened numeracy skills.


My Routine
We have a starting number and a number to count by.  In the beginning, I choose nice numbers, then some that required a little more thought.  Eventually, I allow students choose our counting number and starting point.  I would have expected them to take the easy route.  Not at all.  They like to challenge themselves.  We also countdown.  I like to write their responses on the board for them to visually see the patterns.  When a student makes a mistake, I try to not point it out, but rather, allow students to have opportunity to voice their concerns with a response, respectfully, of course.

After going so far around the circle, I stop and ask, What will _______ (a little further around the circle) say next? 

We usually get a couple of responses, so I allow them to explain their process then, as a class, they determine which one makes more sense.

Also, I like to ask…who will say ______ ?

Side note: Later in a functions unit, while looking at finite differences, a student explained, this is similar to what we were doing with Counting Circle the other day!

Our First Counting Circle – Count by 10
I began with couting by 10 on decade numbers, by -10 on decade numbers, then on numbers like 11 or 14, counting by 10 in both directions.  It was a great way to model the routine.  Students are comfortable with it.

Next week, we counted by 2s, up and down, starting on positive and then a negative.

Several students are all in – they’ve got this!

Then by 5s.  On 15, 70, -85 then numbers not ending in 0 or 5…. 37, 128, -89. Both up and down.

I began using single digit integers then a few double digits.

Next week we worked with decimals +3.7,  starting with an integer, then moving to devimals 11.2.  One student this particular day was quickly running through their numbers.  When I asked their strategy, they responded….its easy, add 4 then count .1 back 3 times.

We also use fraction expressions as well.

I already know my stronger numeracy students-those with “high status” in class (Ilana Horn).  So do their classmates.  What I love about counting circles is choosing different students to explain.  Struggling students pick up on numeracy techniques as explained by their peers.  They are able to see those high-status students’ thinking and realize, “I can do that too.”  Its a win-win.

Yes, at high school age, I have students who don’t want to participate, but with a bit of coaxing, they come around. It becomes a game.  Classmates encourage those who struggle.  We don’t laugh or make fun.  They celebrate when ‘that’ student experiences success.  Most of all, they smile.

Generally, it takes anywhere from 5-15 minutes depending on number choices, discussions, size of class, experience with the routine.

Suggestions:  pre-cal count around unit circle, elementary use money as a context, what others can you share?

Long term goals and planning changes with each group of students.  Having access to learning routines like these allow me to tailor toward each groups’ needs.

*In Kentucky, every student takes the PLAN during sophomore year and ACT during their junior year as part of our state accountability model.  To measure student growth from state data, students are grouped by their PLAN scores, then compared to others in this scoring band.  Once the ACT scores are available, they are given a percentile rank from within that initial grouping.  I, the teacher, can view this and whether they had high growth, expected growth or below expected growth.  The state assigns me an overall rating and this will eventually become 20% of our Certified Evaluation plan.  The other 80% is determined locally and by student growth and proficiency goals I personally set for my students early in the school year.


Time Capsule Teaching #tbtblog #julychallenge Post 13

This tweet made me wonder….


If I created a timecapsule of my teaching strategies…what would I think when I opened it? 

I read the post, Time-Capsule Teaching and within a few moments I thought…what was I blogging about 3 years ago?  I searched back and thought I hadn’t actually started yet, but there it was…

July 17, 2011

I was new to the blogosphere. 
This was my 2nd post.
TMC did not exist yet.
I was learning about standards based grading.

After much reading and discussion with close colleagues and many hours of processing what I had read, I knew SBG would be more effective in communicating student learning.  My grades prior to this had been filled with fluff, things unrelated to actual student learning…the reason some students had good grades but were not achieving at the same level.  Initially, that’s why I started blogging was to record my journey through sbg.

2 Years ago
July 16, 2012 #made4math Monday

It was the 3rd week of #made4math.
These lovely pencils for my classroom.


I did this again last school year. 15 pencils almost lasted until Christmas break.  All in all, I put out fewer than 36 pencils for the entire year.  My daughter helps decorate-cheap flowers, pipe cleaners, feathers-whatever she finds in the craftbox to make them obnoxious.  Students no longer ask me, they just borrow.  It is easier than me taking time out of whatever task I am on to hunt them a pencil. I have a mini clipboard, students signed their name and crossed it off when they returned.  Obviously, some were not returned but that’s about 1 pencil per week.  Its worth it to me, fewer interuptions, I don’t get frustrated if the same ones are borrowing a pencil everyday. :)

The same post I shared this handy paperclip box that I just filled with paper clips before APSI last month!


1 year ago
July 23, 2013
A Reflection Tool for PLCs from @TJterryjo “I have a dream…”


Basically her PLC was asked what characteristics a dream math student would have (in green).  Then, as teachers, what they could do to create that dream (in blue).  At each PLC, they “dotified” what they had seen in students and themselves to see if they were moving toward that dream.

This is something I wanted to do but let it go.  This is on my to-to list for our first departmental PLC this school year!

Join in!
Pick a year. Any year.  Read a post and reflect…
Not been blogging that long? Pick a favorite blogger and read one of their posts from 3 years ago…
Throw-back Thursday Blog #tbtblog

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Get to Know Your Students pt 2 #julychallenge Post 12

 Get to know your students, especially how they learn and think.

Taking my lead from this post, my intent is to consider how I can improve or implement the 14 ways discussed.  In my last post, I shared how important I feel it is to know our students as real people.  This one is to share #5things that impacted my classroom and helped me know how my students learn and think.

My 3 years with Kentucky Leadership Network and my experiences with #MTBoS have changed my mindset.  The work with KLN introduced me to a new set ideas and #MTBoS allowed me to explore with others and develop a new frame of reference as I seek to grow as an effective educator.

I cannot be grateful enough to all those who have challenged me and help me grow.  But as I think of the experiences that have opened my eyes to see better ways I can consider my students as learners, these are the ones that first come to my mind.  #5things for getting to know how my students think and learn…

Wait Time II
I learned about this routine from 75 Practical Strategies for Linking Assessment, Instruction and Learning (Keely, Tobey 2011).  A simple adjustment.  Yet it forced me to really listen to my students.  You can read more on a previous post, here.  Basically, it allows  the students AND teacher to process a student response.  We were all told in undergrad to wait 3 seconds after asking a question before calling on a student.  Some people actually think this deters the class flow.  I disagree. The idea with Wait Time II is to wait again, after the student response.  It allows the responder to consider what they said, the classmates to process what was said and the teacher to consider next steps, questions, etc.  A bit uncomfortable in the beginning, but once I explained the rationale to them, they got it, as did I.  Waiting and listening adds value to what students are saying.

What Makes You Say That?
Making Thinking Visible, (Ritchhart, Church, Morrison, 2011)
A chat with Liz Durkin challenged me to consider ways I could implement these routines into my high school math classroom.  It was the question “What makes you say that?”  that helped me begin drawing out student thinking.  What were they seeing? What evidence supported their statement?  With this routine, I began learning new ways of seeing problems myself.  Students’ ideas, strategies and approaches are way more intuitive than my own.

Notice and Wonder
I was first introduced to Notice & Wonder with Max Ray’s Ignite talk sharing The Math Forum’s simple, yet impactful strategy.  You can read more in Powerful Problem Solving (2013) as well.  When I pose a problem, scenario, graph, students may not readily know where to start.  But they can tell me what they notice.  Its a starting point.  Everyone can share something.  When we listen to what others are saying, that ignites other ideas as well.  And they begin sharing their “I wonders” which are great transitions to explore more.  Its great.  Its simple.

This routine carries over to standardized tests as well.  Students shared how they didn’t know how to approach certain problems on ACT or their EOCs, but they looked at it, thought about what they noticed, connected it to something they knew and was able to at least make an educated guess. 

Friendly Class Starters
After reading What’s Math Got to Do with It? and completing the Jo Boaler How to Learn Math course last summer, I knew I needed to find ways to invite students to think differently about math in my classroom.  Some major a-ha’s and sad realizations as to why so many kids are down on math.  I began with things like Number Talks she presnted during one session.  Amazing how many different ways students can see / approach a single problem.  When I invited them to share their thinking, they owned the math.  This past year, I implemented Counting Circles, Estimation 180, Visual Patterns as well.  These resources were primarily used as bell ringers to get students in math mode. However, there were days it lead to deeper, richer discussions and I was flexible enough to go with it.  My students’ confidence began to grow.  Their number sense was developing.  They were sharing their reasoning without me asking them to.  I saw some big gains on benchmarking and standardized testing for several students and I attribute them to these “friendly” and accessible resources.

Small Groups and Discussions
When I completed my initial National Board Certification in 2002, I quickly realized small group discussions provided a definite means to seeing student thinking.  It was a chat last summer, that made me realize I needed to quit butting-in.  I would hear a misconception and jump to add my 2 cents rather than allowing them to reason out if they were correct or needed to adjust.  I was stealing their learning opportunities! Yikes.  I began listening more-offering questions rather than telling them the direction they should go.  It was frustrsting for some students.  They despised me answering their questions with questions.

5 Practices for Orchestrating Productive Mathematics Discussions (Smith & Stein, 2011) is a quick read that offers samples to incorporate into your classroom. The 5 practice provide structure to help you develop discussion based tasks rather than step-by-step inquiry lessons.

Another valuable resource for me are the Formative Assessment Lessons provided by Mathematics Assessment Project.  Most lessons follow a similar format to the #5pracs.  I used to struggle offering questions that would move learners forward.  Though some disagree with scripted lessons, this resource supported me with sample questions for specific student misconceptions.  As a rssult, I began asking better questions on my own.

Another aspect of the FALs is the way they suggest grouping students, not by ability, but similar thinking – whether it be similar misconceptions or approaches to a problem.  This supports what I have been reading this summer with Ilana Horn’s Strength in Numbers (2012).  She presents how social status in the classroom may actually hinder student learning and achievment.  I believe grouping students homogenously by approach and thinking puts them on equal playing fields to share and build their ideas. 

By observing student responses and listening to their discussion, I am able to select and sequence ideas for them to share that will allow more engagement from the class as a whole.  Students are able to listen and view strategies similar to their own, but also consider new approaches which in turn builds their own skill set and toolbox for thinking.


The common thread is to not to do all of the talking, but to sincerely listen to my students and their thinking.

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Get to Know Your Students pt 1 #julychallenge Post 11

As I read this piece, 14 Ways to Think About Good Teaching, I thought…I want to do it all!  But that’s a lot.  Wait a second, I do some of these things.  So, here goes…

1. Get to know your students, especially how they learn and think.

Its my belief this is a vital part missing from many classrooms.  There are 2 important factors here-to know your students as people and as students.

Have a real conversation with them.
So many times I have had conversations with students who feel disconnected at school.  There is a very cost efficient  solution.  Its free.  Take time to talk with them.  Have a conversation about something outside of school.  What do they enjoy?  What’s their favorite food?  What are they interested in?  What are they most passionate about? And if they are not sure, well, help them realize it.  Listen intently.  Ask questions. 

Encourage them.
I like sharing life lessons in class.  There are moments when they need a brain break from math.  A perfect opportunity to share some insight.  Of course some may think my advice for life is corny, but years later, its those things that stick with them.  The hand…was shared at a conference, I don’t recall the teacher’s name, but she used this in her class in helping to develop a different mindset in her students.


Thumb- Efficacy – This was a new term for some students.  So we discuss other words its similar to, what they mean, hopefully making a connection for them.  In the end, they must believe in themselves.  If I convey my belief in them, this strengthens their I can do this! attitude.  Thumbs up!!!  You’ve got this!!!

Pointer-Consciousness – Be aware of our actions. We need to pause and consider the outcome…is it what we intended?  But also, if we are truly learning, its not supposed to be easy.  There are some things that will be tough and will require us to think, struggle before arriving at a solution.

Tallman – Craftmanship – Take pride in our work.  Stand tall and be proud knowing we have given our very best effort, not matter what.

Ring – Flexibilty.  All things in life will not go the way we want.  We must not get bent out of shape and react in frustration.  But pause, look for options and make a decision that will move us toward our goal rather than keep us stagnant.  Those loops life throws at us require us to be more creative and allow us opportunities to learn and grow. 

Pinky – Interdependence – If there’s a will, there’s a way.  I tell my students I am there for them.  But I can’t be fake.  They smell fake.  I am sincere when I look at them in the eye and offer my pinky as a promise to support them as needed in their journey.  When faced with a challenge, we cannot give up.  We should consider our resources, school, teachers, friends- surround ourselves with peers who will push us, challenge us to grow and better ourselves, so that we can have a positive impact on our school, community.

Afterall, if it were not for my students, what purpose would I have.  It would not be much fun teaching in an empty classroom.

Let them know #youmatter.
It was a Thursday morning. 
First period. 
The upcoming seniors were freshmen. 
A student sat front and center in my room. 
She was wearing a clothespin.
A hug clip.

So, what do I do? I get a sharpie and a pack of clothespins (Yes, I had them in my room-I hot glue them to block walls for displaying posters, vocabulary, student work.) 

Anyone who needed a hug, got a hug clip that day.  Nearly every student got one.  The idea, wear it.  When someone asks what it is, tell them.  Offer a hug.  Pass on your hug clip.  They do the same.  I saw several hug clips throughout the next few days.

The next fall, while sitting in my room eating lunch, I heard the news about the tragedy at Sandy Hook. 
It rattled me.
I cried.
That afternoon I stopped by Mighty $ and picked up some new hug clips.  I wanted everyone of my students to know the next day how I appreciated them.  Loved them.  I wanted them to know #youmatter.  They are the reason I get up and come to school every morning.

I reflect on the years I felt most connected to my students.  Its those who I took the time to have real conversations with, those I was most intentional about encouraging, those I verbalized my belief in.  I didn’t just hope my actions spoke it.  I told them, too.  Teenagers need to hear it as well as experience it.  Good, healthy, positive relationships. And now, I realize these are non-negotiables for my classroom.

Investing a little time to get to know your students as real people – will pay huge dividends in the end. 

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July Challenge #10 Writing in the Math Classroom

Pam Wilson:

Great post by Bridget Dunbar! Writing in Math Class

Originally posted on Reflections in the Plane:

Many years ago I read the book Writing to Develop Mathematical Understanding by David Pugalee.  I want to use this post to record some of the important points.

Pugalee wrote that

“The goal of writing in mathematics is to engage students in ways that require them to think deeply about the mathematics they are encountering.”

He suggested that, writing, or more generally, communication, happens along a continuum.


This continuum “is not about writing ability but about the level of cognitive engagement of the student.”

He offers many practical suggestions for incorporating writing into the daily routine of math classrooms.

Beginning of the lesson suggestions (pages 36-38):

  • Use a prompt such as “Write what you know about ________.”
  • Have students write a short description of how they solved a particular homework problem.

Middle of the lesson suggestions:

  • Have students write an example or draw a diagram or other illustration to…

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